This invention relates to a positioning control system for use in positioning of an object to be controlled, e.g., a sample-mounting movable table or stage employed in a step-and-repeat camera or a step-and-repeat projection printing apparatus, wherein positioning is accomplished by means of closed loop control.
An X-Y movable table for positioning a glass substrate or a wafer at a high speed with a high level of accuracy has been used in a step-and-repeat camera for producing a photomask or in a step-and-repeat projection printing apparatus used in the production of a semiconductor integrated circuit which directly projects and exposes a circuit pattern from a reticle onto a wafer without using a photomask of the original size. In such a movable table, positioning accuracy of about 1 .mu.m is required for a moving range of about 150.times.150 mm.sup.2.
In the conventional movable table system of this kind which effects precision positioning, use is made of a closed loop linear position control comprising a position detecting system using laser interferometric measurement, a circuit for computing deviation of the movable table from a desired position and a driving system consisting of a servo motor and a feed screw. Such a system is disclosed, for example, in U.S. Pat. No. 3,539,256, as well as The Bell System Technical Journal, Vol. 49, November 1970, No. 9, pages 2145-2177.
In this closed loop linear position control, the smaller the deviation .DELTA..times. of the movable table from the desired position, the smaller is the output torque Tm of the servo motor required to position the table accurately, as shown in FIG. 1. Accordingly, there is a region in which control is impossible because the guide means of the movable table and the feed screw experience friction, and the inertia of the system counterbalances or absorbes the torque required for fine adjustment. Namely, in FIG. 1, if the frictional force is equal or greater than the torque Td of the motor shaft, control is impossible within .+-..delta.d of a target value when the position feedback gain is K.sub.1. This remains as a positioning error. If the position feedback gain is increased to a value such as K.sub.2 in order to reduce this positioning error, the control system becomes unstable and hunting or oscillation takes place. Hence, the position feedback gain cannot be increased beyond a certain limit.
There is another method which minimizes the equivalent torque Td of the frictional force, or which interposes a reduction gear system between the motor shaft and the feed screw. This method, however, results in a degradation of high speed characteristics.
As explained above, the positioning error is proportional to the magnitude of the frictional force of the guide means of the movable table and to that of the feed screw. Generally, the magnitude of the frictional force depends on the frictional speed and the static coefficient of friction reaches 2 to 5 times the coefficient of kinetic friction. In FIG. 1, when the static coefficient of friction converted equivalently into the servo motor shaft is Ts, the servo motor is unable to rotate within .+-..delta.s if the position feedback gain is K.sub.1. In other words, the servo motor does not start from the condition of the deviation .DELTA.x&lt;.delta.s. This indicates that, when the feed distance of the movable table is large, linear position control is effected under the state of the kinetic friction, so that the positioning is possible within .+-..delta.s of the desired target position; whereas, when the feed distance is less than .delta.s, the position control is not started so that the feed distance appears as a positioning career.